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`MZ Audio, Ex. 2001, Page 1 of 31
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`
`L
`THE ACOUSTICAL
`'IHE
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`\\ . \
`W- W- NORTON & COMPANY~ INC
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`MZ Audio, Ex. 2001, Page 2 of 31
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`MZ Audio, Ex. 2001, Page 2 of 31
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`MZ Audio, Ex. 2001, Page 3 of 31
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`MZ Audio, Ex. 2001, Page 4 of 31
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`l ' HAPTI!" FOl ' R ~
`
`COMPLEX
`VIBRATIONS
`AND RESONANCE
`
`N.,.. th.t w, l,a,.., di..,......J WIIV<I mot.on, •nd !heir 1r,n,mn>i0<1
`thto<igh the -.!nun, we aie equi...,..J 10 namino ,;\,nbnl 'Y"""'
`wlx- bdiaviar U IDOtt mmplicatftl th.u, 11-~ ...,u.,., n....
`-
`a,mpb . , . _ .,.. the •<OWlkal faundabom I<>< tho -
`'"""""" ol - 1 , ... ..._ .....
`TM VU,,.orin1 S1rhog, St...J/,q; w,,.,...
`11,. ,unplo ,r,t.,..,,. «mPd.,-od .. ,11,,, h•d e«mtially ,,oly ...,,.. ,ib"'(cid:173)
`boa fr"'l""'CJ'· n,,.., ore actually -
`vt'r)' monr l)'Otem, ol 1hl, k!r.d;
`thmp th,.1 ,_,, -,1>B1e con do so !o mo,,, th.n .,.,. "'"Y· The •lrlng
`-
`,1mdlod b , e , - , _ 111pparu i, ..., ,..,,,pl,, of such • •Y•tffn. and
`...,. th,.t ha, ....y irnport,,t1 muoiCO,I •w1,..,,_
`Tn arNll)'>e th, bfflavio)< of the •lnnll &U'd al two ends, w,, make
`u"' of &11 &rti&oe. Wo fint lm,g<no tho &,rd po,nt< to be 111<1,,:d oll' tr,
`luSnlly, rlgllt .,,cl l,/1, but w,lh ti,~ •onoodn In~., olrlng kepi th• um<e
`( lnlhUty may b, d..Rnod u a plaeoao f., a,..)' th,, If ;i 1, onr fo;thc,,
`It do,,,,,'t - - '
`Wo die,, bane the 1oag ,tnng .lready d.........:I In Ch. 3, lot m "'P(cid:173)
`that o """'"" 111<h ., • twililf; fork, • <omxlcnble dh1,...., oof
`
`-
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`MZ Audio, Ex. 2001, Page 5 of 31
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`

`

`The Physical and Ac-oustJcal BackgrouJJd
`on thf' Id~ iii scndinl( tr.111wf'rse waves down the 'ihing to,-.-ard the
`right At :1 p,1rt1<.:ul.tr inst...nt the wa•·e woukl look h.kt: the top curve(cid:173)
`or Fi~. 1(,1) xo,, \Upptnc a S(•co11d ,;ourtr .• , t-oruMcrnl,I~ 1Jisf.U'll'C
`off le, th'-" right. i\ s('1.c1ing II wo\·c ro tl.«" ldt ,tfong tht- ,i.tring, this
`second source has ~xactJ~ Ul-£> .li:tme freqm·nc:y Jnd ,m1plstudo M thc-
`6.nt. .-.o tht.• tv.-o ,, .wcs. lrau-hng m orri~1k Ji"°"hons h1we tJie ume
`01111plitud1\ th~ s.1n1c frrqw11cy1 and hcuc.:-,• t}w -...111(" \1,:,1,,·t·li:ngth. Thh
`\\-";l\"'e would ht· sJM')\\-TI l.,y lhf" ,;e.'<'ond curvr in Fig 1 ~n} if the· 6r~t
`wa'\·e w~n'. .:tb~t. \VlJen both waves are present. we will have inter(cid:173)
`fc.•rt"ru;C, 1111d 1t~ Tt.'$Ultioi:t ampHhldL' Ill .i.uy m~L'.lnt is lht• sum of thr
`"mplihule, of t•,1t-h w.1,·t· at th,11 in~1.m1, In fiF lt11\ tlw hulh·itlunl
`b'a\·eling ,nv~ have been pictured at the insl:ant tht.·..,· woulcl he in
`phase, with crests •nd troughs coincidJn~. Th,• resultin~ amphrude of
`tlw string :•t tlwl i.r&St,mt LJ then A> s.l-iown b) ltw bottom ht·<wy curvt:
`in Fig 1( u 1. having t""iO<' ,h,- :mlph1'ulr of t'1tlw..- tww:ling w:1ve.
`f\'ext "''1? may follow thr- chan,z,.., in tht• ~~em lw picturing lht- twc(cid:173)
`tr,wcliog \VD.Ves nJld the rdltlLmt displ.u:-e·menl of the stnug at suCCM•
`sivt h'IMants during n c-vcJ" As Jhown by ffg l(b), Cc), (d\, uod (e\.
`Tn each represf'ntntion thf' r,o,itiDns of thr wavrs trJl\'l"'1ing to the ri~ht
`,nd to the left a,e shown by the 6rst and second cun·es respec(cid:173)
`tiveh·. Qnd the rdult...lnt dl11.phu.:.l'!mfilt of lh4_, string l>>· Uu.• bottom bnV)·
`nu,·•.;,.
`One-eighth of• c-yrl,, from the -.,..f!il1nin!_t. asshown by Fig. 1{ a) , th~
`fu:,,t w.1xe ,vill have moved one~eighth of a \,'T:1,·eleogth to tltl" right.
`.t.nd tht.· H.•t..·,md WO\."t" a limilar dh\.J.n~ to the left. gi,·1ng thl.' conAb'Ul.l•
`tiun Jhuwn in Fig l(b}. Th1, rc-(ult.ant dfitplaC't'tllent of 111,r. Jtring h
`then like that of Fi~. l(a), but with a snmller amphn,dc
`After another one-eighth cycle-d1.11 is. one-quart,r cycle from the
`lx·ginntng-tbt- ilnt w.aw• wall hoil\'e movt."d .a tot.tl or 3 quartt-r of a.
`"'.lW1f'n1itth 10 th<' right. 01111 the- M'<'nnd Wil\'f' tl,r .'i,tmu d.t .. t.in<~ to the
`left. Th• two waves will 1h,'11 be euctl\' out of pb.i,r 1hr p,aks of
`one c:oin~lding with u., t,ouwi of th,, other, ns shown In Fii:, l(c).
`Th<' rriull in,1 di11pLH•1"f11M\t at thu ili~l11nl is lhl•n l<"l'O t\'1•.rywhff,.
`11lonc thr string;
`Another one~ghth period late'r ( thrtt-ei!lhths of o cycle from the
`beginning}. t•ach lr.l\'t'lio~ w.;t\'t' wiU hav'-" mo\.·ed to tht- 1l0Sitions
`\ho" n in Pig, l ( c1
`11,~ r«-\:ultin:g t.h~pl.tct•mc·nt of the '\tring iJ tlwn
`like that of Fi~. l(b) but in the oppo<it•• .. .,,,r so d>AI po,!tiw di<•
`placement$ in Fig. J(b\ "''" now u~gativ«', and convttsely.
`AJJotl,.-r ouc dghth r<·riod later ( one-l,4lf cycle from the bcg,nnmg)
`r-:u_•h wtwr will h,l\•,· mewed 1o thll" {'Olition'i ,hown in Flg, I ( <' ). Th~y
`arc now back in phn"tt". and tht• rf>sultant di$J')fa.C't'mrn1 ii. now :u it
`was in Fig. I(• I, but again in th., op(l<)<ite sense.
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`MZ Audio, Ex. 2001, Page 6 of 31
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`

`~,
`c,.,,.,,.,,.. n1...,,-•,iJ Re.,_....,.
`
`,.,
`
`'.,
`
`'"
`
`,.,
`
`•
`•
`•
`•
`FNa. I -•••• ,J • ,,.~1 .. u . . .., • ..,_,...,. ,,.., - . I -
`lfowllo• lo opJ'<~lt• J,..,,,.,..,~ Illa ........ (o), (M. (<), idl. ond (ol.,..
`1hoconllrant1oma1 .,-i,,J __,;ghtl,~
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`MZ Audio, Ex. 2001, Page 7 of 31
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`sS
`At ~uc.-cc.'e'tllug one-eighth l'}'dt.- lncrcn,r1Jt5- ll.e ,.a.me t-01uidt-rution1
`will show tlu,t tht• stdug ,ttr~~u•es thr pcu.iUOrtJ (d), (c-) , (h). and (u)
`of Fig, 1. Al lhir time it ii back in its onginal position. and thi' ,-..•hole
`cycle start, O\'tt,
`'[UC re~uh is a motion of th .. ,tr1ng up J.rJd do,~ u in !>I. !leri,e~ of loops
`a.-. shoY.-n in ·Fig, 2, wht."'ft' tltt• M1lid curve \how'! th~ ma'Ommtt dis.
`pla0<m<,t1l m one direction, •nd lho dashed cun·• sho,,,. the dispLce(cid:173)
`ment on<e-lulf cyclr latcr. This llo.d al motion Is c-,llc<l a .tandl•~ """"•
`unet:" tht' '"""'(' is not 1no\·mg tn (•tlht:r dirt-t·llofl along thr.- string. Pr..ie,
`ticolly all mu!licaJ iostrummls ~c.•nr-rok •1..mding w,1' .. <'$, .-~ we wiU Sief.'.
`
`In n .st,mdinjt wa,·c. tl1tn lire- rn-tain points tilong tht" "tring thnt do
`not move; th<:se points •re dcslg!li.,l<>d b>· N in Figs. 1 and 2, and are
`called noclu n,c ,1bnii.ting S(·gme-nt of ,-iring Letw1-~n two nodes 1~ u
`l<>0p. I hll way ht.•twt·t·n nny h\:O nod"' i~ a point wht-rc the ...-ihrill1r>n
`has tho greaten amplitude, this point I• calkd an orrtinodr Points
`marked ,-\ in Fig, 2 indioule pooitio•s of antir,o~e,i.
`Rderri.ng back to Fig J(o), w1~ seir an tmport.ml rt'l,n.lon: tbc dis.
`tmt't" brt\\'N'll two adjaC<'nt nodt-. of a sta.ndln~ ,q.1,·~ is f'CJU.\I to Ont'•
`half wavelength of th• two travelilll( w;l\'es that form the standing
`\YQl,'~
`\.\'ith tht~ lr'lfomatlon wr aft.• ablr- to worl out lhti osclll.1tion {rc.J•
`qtwnclc,- Df ;i srrin~ R%«1 at both ,..ndi , Suppow ib )t'1lgth is f◄ mrkro;
`In the long string, the wavelengtb of the tra,r!tng wa,.,.. depend, on
`the frequency of I.he ~ by l.hc funcL.mtotal waYt relitton gh·t:.n
`In 1''1 (2) of Ch, 3, n.1mdy S = P. The clM.111<0 l,.,tw,•1•11 h•<> ndjo,
`«"nl nodes will th,n nho dop,nd on the lr"']1.1enry Supp°"' ii lo be
`adju,ted until the distmc,, belwe,n nodes is L. Sinre the nodes are
`points on the s.trlng tll.a.t art- not n,o,ing. w~ cao clamp the string at
`tht•-se poinh- withaut nfll"cting tht• \·lbr~tti(Jn n.r th(' ~Cri11g in brtwN·n
`Thr- ~trinp; out!tidc- these clamps <0uld thrn hf, <111 off :mri n-moYcd,
`Lea.fog the siring cl.1111pcd ~t it,; tv.·o end, ,till vihrating, as in Fig. 3( a).
`,,,., fre't\lfUC)' or th11 ,;bratioo rn.11y 00\'t' be oblaint..-d \'tty simp1y.
`Thl' two 6,rd «-ud, (lf lh" string nrc- nodt'!., nnd 1lnC'C" thfl di1tnncr
`between nodes i~ hn1f the 1h'll\'elength A1 or the tra,rdin~ Wl'WM pro(cid:173)
`ducing this standing wave. we ha,·o
`~, =2l..
`
`(1)
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`MZ Audio, Ex. 2001, Page 8 of 31
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`

`

`..
`
`"
`
`c ..... p1n \·;,.,.,,.,..,, " "~
`
`'"
`
`,.,
`
`'"
`
`'"
`
`~-- &- tt. /,,rd rd *••~ ..-1.11.., ,... N.w f,"' Sil,. wbM
`/, ,. Ibo• ••'- ft..,1,,_,. i-od.-inC tho .... ,~.....,i, l, 11......, .,.,.
`
`'"
`'
`f
`' .. it.
`•• the frt'<l'ff><',- fo, 1),d v,br,MII """"d In Fo1 ~I•). TI,!, ii t).,
`I~ ' - wlli<b -••n;.t St -
`loop ol t h o~ - , , . -
`fu"'1aMe014/ "'°"' ol U.O itrmg. S"""' ,1 .. , spt«l S of,..., .. "" lhn
`Ibo~ Thn r-,t;,,Ja, "bn,toon .. c,ollod Ibo
`tt,,, -
`-
`'"
`
`,tnuH ,. p,en by Eq 11} In Ch ,'I, we n••1 wril, lhl•
`
`Thi.. th<n. 1, th, fu,,,1,.....,t,.1 ,•11nt,.,.. f,.,p"""')' .,/ • ,t,m& ol lrn~•h
`I., &,c,d ot hoth end-. 1,o,-,n1 • _.. I' \,lognm, P"f ""''" ~tb ...d
`,1tt1,h..d w,th • ~ T -o,»
`TJ.,.,.a,,1 th,..J.,·"·A)' th,, llri..i ,._d <Obn•r. s,,..,._,.., • - •
`"" r~ a1 -.1i.- m ""' lomC ""°' -1 ,..._-.. ttw
`""""°""
`Jaapo mon1 ... ""' fit ...., m lhom ,...., th, 'I"'"' -
`or In F,g. 3(b). Tl•• n,-w wovel,ngth 1, now g;,.,, \,y
`L.
`A,
`
`(~,
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`MZ Audio, Ex. 2001, Page 9 of 31
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`

`

`6o
`
`Tl1<1 Phy;ical and A«11utkal l!ackgrou11tl
`
`(5)
`
`s
`s
`1, = = 2 = 2f,.
`~I ..
`L
`1 hi, I.\ tltt• t\t•:,.l \tbr.wou ntoJt• ol tJ1-.• 1,trfo~, and h )1,L, .. rni1Ur:-Q<.')
`•·\1u·tly !wit:t• tht.• fonclunn1htl
`SimiJJrh-, "e ,nay increa.~ tF1e frc·qm:ncy until three loops of a
`st;"tndini; ,,.i.vt· wUJ fit the string. frorn Fig. 3(c) we ha\e
`1, - 11,,
`1.0 tht frcqueney ol this mode ts
`f. =31 =3f,,
`2L
`or t.·,at.1ly thrt·~ tin1P~ ,he!' hmJ1imcnUI JI 1ghl'r frl-qutnC)· nlodes will
`h<• fouritl in I hr s:u,w ,, a,
`llw )lrmg: !itrt'lc-h<•d h;·twt'C'n ,upJ"l(lrb can thus \ihrntc, in a number
`of mocks tl1:il are n.·l.tted qwte Slmplr The frequency of the lowest
`ur h111d.mu·ot,1I mod<"11 1:,, gl\t>n by U:l 13 1 i,bove. lht' otl11.-r mod1.'1i
`have" rttc1un1d,.s that arc lnlctg,rt1l m11ltlplr.~-th1t 1$. 2. 3. ◄. and so on
`tim"" the fundamental frt'Cjuenoy.
`
`•l
`
`(6)
`
`(7)
`
`lmpc,Lu Trac,~linf( m1 o String
`Thm• Is anotbt-r way of workioa out thfll vlhr1Uoo fn-quf'ncit~ of a
`•trin!(, which may be <'>Sier 10 vitualize thao the anolrsis -used above.
`Lei us again rooslder LIM' string of length L stretched horizontally
`lx:twrt"n two 1upporb with .1 tension givltlg u sptcd S £or ,uvtr on
`the, string, Sur,ro~· now we $btrt :10 impul,;e- in t.hr form of a hump at
`on,. end or lhe •tri1'1: by moving the rupport quickly upward and then
`bnck again, as ibown lo Ftg. 4( a. U) th,- smJ.ll .urow~ •I end A. ThlJ
`hump will thrn tra\'t·l 11lo11g tlt1· Mring tow.nd the uth~r uapr,ort B
`with lhc Sj>''ed S; wbm it reach,-,, 8, it will be r,8ected. The rtOt'ction
`proccs, tao be vlmali2.t.'() by ima,gining for the mom'111 that the string
`Is 001 6.,ed lll lh< support 8, but nleuJ.s p0>t I~ a, ,bown by the
`dottrcl lin( in Fig. I ( h ). ,md th1t thrTf' h au iovrrted hump of the
`same shape t:ravt>lin,t a.long this cxte-1u;ion bar\- tO\\-iilrd iupport A.,
`.a:rdving at J3 at tbt1 same tith~ as the· onsr;in.11 bump. The hvo },umps
`wUJ lht'1I c:,lut.,·J e-.ad1 orlwr nl pe>inl B, !O this po[nt on the 5trlng will
`QrJt mo\'t'. Srnce ii dn,•~,,·t, it cnn \it;. f.1stM1c-d U>f~ht to th,· support
`without cha.nsrtog tht> wav the hump, mn\'C. H follo~ that the imp"l"e
`r<•Arct«l r,t the fi"-d .,.pport B w,11 be in\'l'rted. llllt i>, ii will rcftect
`-'S • dip ln1tr1td or M l1ump. TI1iJ UI 1;hown hi Fig. 4( C ). The dip of
`Fil;:,., 4(c) will nt)w tra1.:t'J hnC"k towird th~ Br~t tuppmt with the UJnt"
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`MZ Audio, Ex. 2001, Page 10 of 31
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`

`

`Co,r1ple,: Vibrallmu arid Re.wna"°"'
`
`ti
`•
`
`"'
`,.,
`
`• -
`
`",
`rtnog. {b) It .....i.,, Ibo otb<,-,rnl, °"" (o] 11 b r,R<lcled o, • dip-ad
`
`Fu,. 4 (o) "" fmP"loe 1,, Ibo form of • hump i, mrl<'d .km■• ,tro\ohtd
`
`of• h=p.
`
`rpoal S, When It get, the,-,,, i! will ogair> be ttllected. The mlected
`lmpul"' will nDW be a hllmp Ub tk original, and tho whole proress
`st""' mior. Tho timo for a,,. rwml bip al lho lmpui.. will he ll,e
`tl""' U./S n,quin,d for Ibo lmpul.,o ID lr•vel ,wi.,., the length of tbe
`,Iring, 0000 ocro51 and hocli. Th'f i, the period of !hill parti<,ulor v:ibro•
`lion of the <Iring. It! frequency wiU ther, be f, = S/2L"' in E:q. {2)
`ah<w<o, and "" "'''""P""d< t<I !he fundamOlllJ&l n!Odc I)( v!bnijo,, al
`lhutriug.
`S"""°"" n""' ""' start an lmpul.., along the >IDag a, befone, orul
`the,, ,wt ■ oecoud <mo tho !nstul tho l!nt 1w beea rollectod f,om
`the athor o,,d. Wo will thou lw1-e two lmpni..,. oo tho ,tring ln>t<od
`of one. ~ tlme betw<eo or,lvo!J af ,nu:ce&,i,,. impul,e,; ,t ooo ond
`af the string will be hill a., ~ " ' l,do,..,_ •• tbe frequenoy of tlw
`mod,, wH! be twi"" "" ~ . Henoo It I, 1w!oo 1M fondomental
`lrt,quoncy, co=pondi1>g tu F~!· ( ~) •bov,,. 1f wt1 ~•mille the """'°'
`of the ttriug, ""°'" tho hump going ooe way p.,.e, tbe dip going
`the otber way, we will 6nd that again the twn lmpubes enctly
`caIJre~ oo 1h01 tli,, <>enter af tho 1\rlr,g 1, not lu motion 1nd t, =•
`,equen~y a node.
`SUlli!arly. ""' c,,, OW't a ,erond impulr<, when the lirSt I< tw<J.lhird<
`the ""'Y alDng the ttrl!,g. 000 • third <Pl<O when the !leroDd 15 two(cid:173)
`!hW. alung. W• wlD lhen h•.., • vlhr•~•" f,oq.,..,cy thrtt time,
`thol of tho fondomcnbll, =ruponding I<> Kq. (7) ■bove. In• .<lmilo,
`faduo"' we con obtain /n,qmmeles -t S. and .., "" time, that of the
`fundarrumttl
`
`MZ Audio, Ex. 2001, Page 11 of 31
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`

`

`The Phy.;ical and Acou,tical Background
`
`Complrx Strint Vibration,
`A 1ncdmrn can carry many \\--aves simultaoeousl)', a.i. we stated ea.rUer.
`1.0 d1l' i.trerd,.-J ~lring <'an ,,bratc in m.1n}' modc1. ilnmlt.mN>U~1r. Jr
`we- wt thr ,trin~ into .,-ibmtion l>v p1mling it-that h by dr.1wi-ng it
`lo om, side nnd sudden Ii- releasi n11 rt-all the modes will be present.
`with omphtudes tb.,t depend on the point along tho string at wblch it
`wa1 plu,kt'd. Tht• cxhkna· of th1 .. \C modn m.-,y b,• shown quik c.mly
`lf we touch the \ibr.1ting stnnJt at somr point. tht• \'ibr.1tiom will he
`stopped for all except those modes that ha\'e a Mde at the potnt
`touched, thtse can kc-cp on vilirab1tg. H~ncc• If th~ string i!I. pluck4..J Hl
`wuw r ,ndom (k-tint :md th<•n toudu·1I ar the c..·nlH, it will 1w found
`that the- serond mode U ,1br:ui11g. ( Thi1i m~r lw d,·krminrd hy noting
`that the pitch of the t-l'llitted sound ris.t·,. .an «tnve-, so th:at the &e·
`qufficy UI hviu• 11.s grr:tt, we will (l,scu~, 1l1bl 111 Ch ~) SimiJ.U'I~'. if
`we touc-h thr ,1br.-tlllg \tTfog ,u ont-•third 1hr di\liUIN" frum on~ l'"nd.
`the third mod• will h<' found lo 1" ,ibrotm,z. I Tho pitch rises •
`twdftb. 1 ln gcncral, th,·n, the )tr-etched .-.tn~ v1bratl->S in a complex
`r.uhiot~ with 111,\11}' m()(lt•-. .,nd fr<"'(IUt'fK.'i•' prr.st:nt 5Ulluh1U)N)1JSly.
`T£ tht• i.trinA t~ ph1t"l,t•d ,ll ,I rolnt ,,nd th,~n h1U( hNl M that Un1C'"
`point, alJ \'lbration, ~top complettc>I)' If this poinl W<'re- a nod~ for a
`ptU'ltcµLr mode, howcv<•r that n"YXlc· could so oo ,1br~tlng. The fact
`lh1H 11 dat•, out do -10, h(N't'\ ,·r, nwoln'I tlut tf tht• Jtring (!' pluc~c.-d at
`a point that is .a node for R ('>1\rticul.ar mod•· of vibrntio-n., that modr:
`is not produced.
`(Just as the vlbrotlou p.,ttun of the pluclc,d siring l< a mltture of
`all tht, 1hmding wav~ modet in vou')ing arnCMmb, 11.• dUcu1.,<"d nho"C.
`io a ,;rnilar way ii can be sbo,,,., that thr <ln11lr fmJ"ll<e. «,a,~ling
`back and forth aloug U,,, siring ln th• ~•mple gi,..., abo,..,, is a
`oompl"' vibration which c.in alw b• mlld• up h)' adding lndlvldual
`standiust: wivf'I" If Wt> add at.anding- wavN of frequencies f 1, 2/1, 3ft,
`and so on, of properly adjnstt'd amplitudes and phases. we can bmld
`an lmpul,<' of pra<:lldllly any <wipe we please "hich I., tra.'Ollng back
`and forth along tll4" sbin,t With thti Cundnmt·uta.1 frrquc·ncy fa. Simi~
`larly. tht- two imrmlses In the- s<.>C'Ond ex-amplt ahov.- Nin be mad~ up
`of standing waves of ITequenci<'S :!(,. ~/,. 6/1, and so oo.
`(Th• complox string m()tion, diS<:us,cd here ue examples of a
`r«mom th!'Otl'hl [doe tn the., nml-ht"n,alid:m Fouric.rJ wltich ,rbltts that
`any curve of arhn,.,..,, thape [ .,;1hln t<'rtlln libmu limilll) which
`repeat. periodically (a11d hrnce has • wavelength >.] oao be repro(cid:173)
`ducrd by addu,g•11u1W1dal curves QI wavelengths A., >./2. ~/3, J./4. and
`so on, with propc,rly 11djmt,d amrlih,d.,, and phLtes.)
`
`MZ Audio, Ex. 2001, Page 12 of 31
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`

`Co11111ln vu ... ua,,, .. and R""111<ltlCll
`
`vo,,01iog ,1;, Column,
`TI,o long olr column will """'"';' 101,~ilud;ru,I w,.n, ju,i "" tho long
`,tring "ill trommn tranner.,. ,.,.,-0$ If we <re•te two wases ol equal
`omplltude and frequency movlo>g_ In Ol'P"'ll< dlro<tlon, In th• column,
`we wUl uhtllln n kmg!iudlnol ,landing who ln IL Thn a,gumon t la
`ffmilu le, that for the rtr!ng, IO "'" =d n<>I tef"'"' II, Fig. 5( o l 1hoW11
`
`•
`• • • • •
`• • • • •
`• • • • •
`
`•
`•
`•
`
`•
`•
`•
`•
`
`•
`•
`•
`
`•
`•
`•
`•
`•
`"'
`- - - -- -
`-
`•
`•
`, ., • • • •
`• • • •
`- -- -
`-- -
`• • • •
`
`•
`•
`•
`
`•
`•
`•
`
`•
`•
`•
`
`• • • • •
`• • • • •
`• • • • •
`
`F!G. 5. L<,,,gi'11dinal .....,.i.,; wave In an U, ,:,,lumn . (o) At 11n In<! ""! ol
`1'lUlo\""' w,pi.,,,.,..,. or u., ..,_ ""'lo""'°". (bl One-hoU oY<lo lau,,.
`tho"""~Jll>'1ltion< of• few choseu lllr m1>l"<'Ules in tha column for ti,.,
`!nmnt at whlcli \belt dl,pla"'"1lellt. ore at a ma.,Imum, ood Fig. 5(b)
`thow• tho m.ollgwl>tkm <ln"h•lf ey,elo later, thooe Agu,o, com,,pond
`,o the .. ,,.., pllrlo of th<, cycle"' f ig, l(a) ond (e) re,pecti,'tly. Tho
`po;,," morked N an: 11,o node, of the ,i.,..Hng wave, being placa
`whore th<: air doe> not oscilloto.
`Tioe gtaphle ,epru,.,!a!lon o)I Ch. 3 moy bo u<od to ad...,t•gc horn.
`W e pk,t th< di>J>J..,.monti o, gl...,n by the o!T{J"" under Fig. 5( •) ond
`(b) agaimt d!Jte.nre along the oolumn. We thrn get Fig. 6. wh€re th<:
`
`,
`I
`•
`•
`•
`F.,, 8. C.-.pl,ic ,.,,,,..,.,._ ol • b>gitu<lln>l """dlnl w,.,,
`
`I
`
`MZ Audio, Ex. 2001, Page 13 of 31
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`

`

`1• 11.\l'Tlill J11,• 1; ~
`
`THE EAR: INTENSITY
`AND LOUDNESS
`LEVELS
`
`w~ luivc uow ,t .. ,;lopocl the phy,kol ~oo """"o;.,,I foundation> f..-,
`d,,.,_;.., ol the •=>lie of music. -"' th,t ovenhaally ""' m,y e,.mim,
`th, ?hi...,,.! <>Oh,.,i<>,- of mu,k-al irnlnlm<nt> .. - - ol ....,i,d,.
`How"'"'· we cannat do thi> properly until we h2'~ loomed a httlt
`llhou! the h!_,.,,.,..·, reachoo to the.. ><»m<I>, and th!,, 1n,,,.t,.,e, tho be,.
`h,,-r..- o/ lh<,,-ptor 11,at "" call the""'· 11,1< wgan i< o v!W I"'" of
`~ mU>ioian"s "'-!ulpme,tt. ,i is .. ocmpU<>.ted -'-"d"' llulo uod,,.t<w;,d
`a,, ""f <>I hi> 1,,.,.,,,.,,nl,.
`s,,.,otun ~I th, Eu,
`Tho ..,,,ml •PP"'""«'-"'"""""• and rcl:,l.<ln>hlp of ti,. v,irl<n11 J>brO,
`of th<,...,.,,.. di!S<.-ult !o ,1,.,..-;,, • li""7tl ,q,n,,;iuou,m. rndi drowlog,
`on, ,.,,.;1,1,]d in ,n<- h•=rnr~-' fo,- ""' """'°""'• • "'homJtje dQOgnun
`"'n show btu...- the ttlauoo>hip .. d fonobanlng nl the~ .. ...,_, p,ort,
`nf th~ ear; tt.l, i, !(l•"<"n In f'3- 1
`For d=lpti,,.. pmpo>e>, tho oo, io dJ,,ldrd ttito th,,., [ID-rt., the
`m,ter. ,1,. ,.;ddl<e, uld the !Dn<T ""'· Tho ou"'1 ~"' beg,n, wi!b d,o
`obvioo, "'"'""I po,t ,,._u,d lh< '""""• whicl, ..,-,·e~ IQ """'""''"'"
`,,,,.,,d """"' .. ,no,wlu,t l•ta 11,o ~"""'"3 .. r th .. •udll<>rl' C'OM!. ln ,..,.,
`
`MZ Audio, Ex. 2001, Page 14 of 31
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`"
`
`Thu ff<:c,,ptlcm of Musical Sou11d<
`•nim"!' I ond sam,· l""'!'l• I the pinna 1, ,.,,~obi< l<> holp rollo,:1 >Ouo~I.
`htH tho l,um,n 1>lruw h•• "•tu~lty b"'°"'• '"11,c, u>clW Im ohl, pu,-
`1'""'- 11,eu",/il"'Y "'""' (,I.,, eallr.l the.,,,..,,.,) iu r.ubo •houo th=
`"""""'"'"'' l<>ug. which iO cl<»etl 01
`'110 In""' ,·nd by • m<mb,ooo
`called theoon/"'"'
`On ,he iruide ot the oo,drum Ii ,1,., region of the mu/di• ""' It;,
`<:<mn<cted to 1in, hool of tho th,,.., by• duet c:olled the. F . (cid:173)
`,u~ this alkm·• ohon~" in th,, .,.,btent air ll'emire to he equ•II~
`and not couse lorge distortkln> of the =drum. Tue middle oar <:O!J(cid:173)
`ta.ina a chiUII of three >IJWI h<>n<>, csll,d (ho .......,ular ohmn, ond
`ronilitiog o! the. M-=, t~c ~noll, and 1h~ ,11m.o,,. n,..., on, OOII•
`n,ct,J to eoob otbor u d11,,,.,, In p;g_ !; th,.. '"""""Uons ""' no!
`rigid. Tue hom1Dtt r, roruac-c•«:d to Th< ~>rdn,m ,o u to mov<> with I~
`At tho otbrr ood of tho o,,iouLu ch,111 tho ,dm,p I, •llacbcd to •
`""""htano coiled <he ot;OI wlt!dow.
`
`__ .., . ..,. -
`I =
`' '
`'
`~ "" .. 'l•-----.. •fl';;" k-------- "l!ll"-------•
`
`111< lnn<r CIJr Ii, tl .. 1 portion Jn;Jdo the oval window. It coMUll Ul
`p,<rl of•""'~'.'" I" tho ho,,y ,iniot,,r< ol the ,kull mlled the eadth!o,
`wl,ld, «...-nblo, o ,,..;I Ulell In gen«ol ,l,.p<'. 1,,,,;ng two ood ~,, ...
`q""""' h•m• 01·«011. Far ..,.,,·,m{<,1oo,,, th,,''"''~"• lu1> been .t,own
`1trnigl11cn<"<l ,,.,, In Fi 11. 1. It b GIi.,! with, Ruld (tl"- l"'tllymr,I,) •nd
`1, di¥idcd down ii, longtl, br • ,oft l""tm,m «1ned th, /,,,,.;i,,r mrm•
`/>1one. Tl,;. form, two long eh,m~ m>< of which ;, "'P"'Oled fram
`lhe middle""' by the 0>-ol win<k>w ott.ehed 10 ,M ni=P- The o1he,
`diam\-,,, 4 ..,.,m1ed from the mid~I< .._, by :ho""""' ,oindo,o. The
`lw<l dS\mh<r> are oorm,cted toj:tlh,:r ol lh~ far eOO by a Jmall opening
`!nth• bo;i]o, membrane ealled the i..lJoatmna. So""' 1hirty-thOOl'IIXtd
`,,.,...., ... ding; embedded !n the lwilar momlm.ne erue dlsrurl,ance,
`
`MZ Audio, Ex. 2001, Page 15 of 31
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`

`.,
`
`in ii •nd tran<mit thlr inlormot<1n "' th• J,ru,,. A,....,hod !o lho mohloa
`(b<,t not ,hown ln F\1, l) "" tho •-""'"• co .. ,1r. Thoy pl•y""
`rm in hearl"ll, b,,c m.,.,,"'.., "'up and down ..,doc,""' .....,ij,J
`In malnlaiQlng equilibrium,
`S«md ,....,. fro,n tho oobide alt I'.,. down ,he audito')' oa,101 to
`the et.rdrnm, e,e,-Hng "" ahemal!ng premue "" I! or,:! «I\Ulng It 11,
`,ibrato. The .. vibratioo, ""'- <rammitt.d through lh< nosh:11!01 <:ha!n
`tt> th,, oval willdow of !ht mcbl ... Th<> ""''-"g,,>)C<lt of tho bmt"' III
`tho oulcular chain provld .. a~ <yrnm. In "'ch • si·51em, • mudl
`foroe ooltng over a lo,ge dlrtan<e ot """ e,,d ,;/ tho ,y,lelll generate,
`• luge lot"" acting ov,r a ,n,o!I dl<le.nce ol 111< other ... d. o.nd 00.0•
`.......,Zy, In ,ho ear, Ibo fo,,,., ol tho .,,,.1 wfaxlow Ir obrut J;:J 11n,.,
`tho loroo on tho e,udn,,n be<,u .. ol lhi.l ~ u.tlon.• The f<><co""
`th, Nrd,wn wiTI ho ib oreo mul!lplli,d by tho Jm,nd r~..,,e on ;~
`Thi, for.,., mulrjp]ied by the faolor 1.2 d"" h> tbe k,..,, o<mn of th,
`osslculor o:hain, Ir appliod io tho o ... l window. ond wm produce •
`r= in the l!uld bth!nd ft. 'Thls prem>re wiD l>,. the force on the
`oval window dMded by ii> orea. Since the oreo of tho eardrum ;,
`~ b l y larger th.au that of Ibo ,wal window, tbe remit b a -
`..,,. In the Ouid ol the o...:J wln<low ,o,ne 10 to 20 ~""" th>t on tbe
`••nlnnn. depmdlng"" ir"'l.umcy.• The OIOtlon of tho O\'ol wlnd<Jw
`II lo,. thJui 1lu1 oI the eo,drum by th. lo.oto, La gl""" •b<we. bt<,o.u ..
`d. <1,o 1o,...,, &<illm ol tho ...,;out., ehaln. Tho .,.._...,..,1 of th!.
`"'"'1n u .. ,ch tho• J.,, ,-.,y 1 .. ,d ,ound• lb. mallon of iho OV>I window
`a,mp,=I to Chot d. •~ eanlru,n II ,edu«<I .cm furChor-; th1' l,,o....,.
`tho lihlih,:,od oI oa, dornoge from "''Y loud ..,.,,><t,.•
`TI,,, in,m,,. oo lhe .,,-.I window \1 onuumitted ,u th, odi'"'""'' !h,ld
`irnide thP «><hi.., Fluid, ore qtrlt<, i1,eo,mpre,;ible. •od tho hony ,tmc(cid:173)
`n= in whieh the ""'M"" II in,bttk!cJ "qu;te un)"lokllng. lime,,. to
`allow th< Hwd to """" wt.en P"'"""" ;, •pphed to the ov,I window.
`JIH, n;nmtl ••Ind.,.. ;, µrovidetl. Tilil 1'1,n opening covered with • mem(cid:173)
`brane whl<h rnn Y"ld under p,..,wo. A m<Jl:lon ol tl .. <Mil window
`lownnl i< •=mpru,led by• motion ol oho "'""d w,ndcw outword,
`t"!!Mh'"' w;tl,, Motil>D ol \M ..,,,W,,.,, Owd. Tl,e HWJ n,c>t ,on• in turn
`pn)l),,co n>:1tio1>< in 1M i,...;1., """'h"'""' 1hc,.o ••• ,en,;ed by the
`"""" end;nll' ,.,,,bo,:Jd,d !u ,i,. membr.rne ond cho rm,lllng ,Hmul!
`(t.>n<mltted to tho bniin.
`A ,,..,,t d<0I af w..-k ha, b<,,n d,me l<I d<tonnl"" tho mottnct UI
`which the basilar """11hnu,r ,;brat .. w!wn ""md ...,,,..,, ""' =ived
`by the ea<. It ha, now be.,n cstablisW that when the eardrum nd
`hene, the <>I'll! window are vibnued • • • ,i,,glo frequency, ,. • ..,. .,.
`p,,..Juerd on the \,a,IWC n=bnme wl,lcl, ,,.,..1 olon~ !1 owoy f1'll!l
`tho two! wind,w,.1 M "'"" Jndivldno.l ,...,,.. "'""°'• It< unpUn,da
`I.a,,,_ untU the wi1,-., reo,he, • e<rnln polot o.loog ti,. ,,..011,,..,,,.
`
`MZ Audio, Ex. 2001, Page 16 of 31
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`

`The lk<.-cp1Jo1o o{ Mw.ical Som><.!•
`
`go
`alter which its amplitud• quklrly dfminishes 1110 point alon~ the
`mcmbn.11.e at which th<' greatest iunphtude 0Cc,1rs depends on the
`frcqneney of vibration; for hlllh lr"'lnencie< it is d0$e to the o,:u
`window, and lor low frequencies it ii at the far end of tho membrane,
`oear t.h• hebcotrema. Tb<: d,_<pl.a~menl llk,u~ tilt- mc..ubr.uot· ol the
`point or g,<!.ltOSl ,mphtude mc,.su,rd from th• far ,nd of the mem,
`branc. ( the h('Jicotrt-rna) is approxjmatd)' 1->roporUonaJ tn tl1t' 10~1:uithm
`of tho frequent;-, ii th~ froqu,11,y i, clouhlrd (whi<h locrea<~ th•
`pitch In n.n oc:tnu~·, .t.'I' wiJI he nppurt"ut h, Ch. 8), the pnfnl nf ~te<t
`lllTiplitudc mo,'ts:s 11,mg th<' ha.'fflar mrmhrDJW" ihouf I millimrtf'r,
`cll)l.rr tn tht' oval window.o Thr '605" of pitch (rt>l.1tf'd tn ,-ihr-atton
`freq,1encyl i< thu, partly rlrierrnined h)· th<- plac,, aloog the hl,$ilar
`membrane where the vibration runpliblde is L,,~esL There must be
`other !actors also. sinct' for ,ounru close togcth,-r h1 frequency,
`especWly ot lo"· frequenclc-., the diJle,.,nre in mi>tion of the hosiliu(cid:173)
`memhrane does ool appear great enough to nc:<ount for the pitch
`discdmlnatlon of n good mu.icl411,
`'J'btj sigJJ.als tr.uumitted to the brain b} the n.tn·t-.s l:D1beddrd in
`thr has.Har mctnhrane undergo a gl'flilt clrnJ nl further proCN1ing
`in thir hrain in ord~r to pnn·Idr tu v.'ith fh(' information w,• ~r..t from
`th<• 1ound1 Wf'! hear. 1t h mottly in this fonhr-r flrocf'~ing tlmt pitch
`di~criminatioo mu-.t take place. Th(' dt•t.JliJr(l 1tn1Ctlll't' ood behavior
`of th• nerve <0nneclion.v he!w...,, the lnne.r <'tr and tho brnln is quite
`iml"'rfeetl" 1111derstood and is tbe rubject of much inw1ti!!9tl<m.'
`On• fnterestiru; resuh of rel'<!llt in•esti~•lions i< the lindlng that fn
`most J)t()ple <ptteh sound,; are processed 1005Ur on the k!t hrmiSph«~
`of the brain, len,log tlw oth<er hemisphere, with ,ts !deulical auditory
`nctw(lrf4 frt'C ID h .. ulJ(' otht·r incc.unJng: UilOflll..1.tioll suth u music~•
`
`Binm,ro/ U.lm&tg
`\V('I SM'lcnll\' br11r :t0t11KI, "',.1tl1 two earl. 11n& "<» 11hliu: binnurnl
`lilt<-nfo~.• 11Jf': ,!iound W'1.\'l"!J rraclling lht" h,-n e,n .. , .. ;n ""Ullh• not bt1
`idrntk•I. For low frl'<Jllf>flO)• ,ounds, ol lon~ wa,rlrn!!lh (co,upan'cl
`to th• •l•• or the bead\, there will ~,..,•rallr I,., " pho<r dilfrren""
`due to lhe sli!lhUy dillett'nt arri.-nl time, of.the ,ound., at the two cus.
`For high fr<qum<y ..,uods. of dic,rt '""'"'length. there will nho 1"'
`an 1t1t.n,11y dU!crcoc:o, due to th., fact lrull on• ear if farther from
`the .,,urce of the sow,d au<l lu the ,ound "shadow" of the heail,
`llowe,·•·r. d<'Spitc tht'se dUieren-ces. we wunlly btM o:nly one sound:
`this fs bll>l4ur.i f1uio1L lo th,• J)T0<('>$lug or these 30Wl<U, ""'""'"'·
`lht:i hraln uulJ.,.1.~ the dJRrn·ocu to <:J.uthl~ t.L, 11, trll !rnm ,vh.tt dJrc<.'(cid:173)
`tion t"hr 1ound t, comin~. 1h11 b1 the prOC't'ss of fr,caJIJatlon. wblch ii
`II•~ ba,;, loo tl>I' rtrrrn1•111t,r/l' rffrct uttllz,-d in high Adellty l()und
`,..r,rodut'tloo nnd di!t'U.ISOO £m1hrr i11 Ch. 15
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`MZ Audio, Ex. 2001, Page 17 of 31
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`,,
`
`So"nd /"Jcnoil~ ond 1/rari"!
`The cot I, on e,t"""d)' ..,,..;t,,e Uevloo. To= how....,.,,.,,., kt uo
`du •n "!"''''""" ,,,.~, sauml ;n1m;lt1,,. lu C"- 3 ,..,. ,,.lt,uL,«<l ,h,\I 11
`..,,,md ,,,,...,.. of an< "'"" would prnd'1<'o " ""''"I h"en•itr of !~ · •
`wott, pt,r ,qu•r< mete, •• ■ di>IOD"" <ti Oppr<l,;motoly thr,o ,,,,.,,,.._
`(Th!, di>tanoo from • ""°n.d """"' in the OP,,l'I w!TI giv, ln!on,llie>
`<:<>rnpan.blo IU d>oioo p<odo<ed hy th~ .. n,e ....,,oc In .., ,ver,ge ""'1
`ot: tth<>.<ttl hall."'""' "ill ,t,,;w in Ch. 9,) SQlo, th< r'l!>[JOHi< of tho
`ear to sound, depend, on frequency. let uo """""' ..- 1 ,tarting !'O'fll
`the rother irrit.tin8 lr,qnency of 1000 b,,<tt, ,since lhi, ;, • mmdud
`fn,quency fm m.u,y oudio ""'"'""'tn""'ls, We wm ...,,me lh,t""' ue
`list..,Hlg ,.-Jtb both,.,._ We wtll /,u;thc,- !Wumt that th• wur,d 1..,.
`lon~or ,h.,, obo,,1 a h,11 • •"""'<lo fo,, "°'"'d; of ,horte, dUntlloo th"'1
`th;<, ,ho reopoo .. <JI !he...., will d"l'eod O<I !he dW'l\~on."
`If,,., """' h,len 1<1 tl,;, ,oue<l intew.,ty nt 1hi, fr<"'!'""'''Y• ,_,, ,,.·oulcl
`judg,,;, To b,, • ,-,~)' a.,,,~ oouod, r.11h<t ufl<'<mlf(lftnbl~ "' ~, ll,!, fr,,
`q,,mey. The mu,1"'3n ...-,..M eoll !t fl!, y<1 ii t, pn;,du""'I by• '°""'"
`v,·hc,o,, p,:,w<t. bl mdi"",y evo,y,l>y S!.,ndo'li;, ;, q'llt<' m»ll Now lol
`U< ml...,o lho intemitv bv • factor of l~, rith..- hy mo1·in~ lho "'"""
`"'• dW.nt< of 30 met= or by lea11ng ii ,..h,,,. ;, ii •nd red"<:it:ig i~•
`I"',.,., !o 0.01 w.ilt. The intensity i> oow 10-• watt, per Jqu""' "'"""•
`!Jut th~ !ICll!llll <11ll oppe.,ra lu ho ijmte lautl--on th, order of /~rto .
`. •,nolhe,- belor nl Ultl w;n brinl!I ,!., ,noonsily d""'n !u 10-• ...-.,tt, JJ"C
`.,.,...,., mttor. ~o,d ..,,... ,i.., ""''Kl I! hirl• iaft-on the mde, ol p/000.
`,\noll1<,r factor of 100 "·ill gel 1hr (ntrmit~ dowo lo JO
`' watt> p<<
`"lu.i"' ""''"· wl.,,,., ~-• WOtlld 1u<1go It 10 bo ,·ory ,oft-<1t, d,o m&r
`<>I ppp Our m.-ful m"-'lcnl ••o~o of <nund in1<rurn,. h thu, ohrnll •
`milhan too,.,.
`Tho lnl=•'>" of Jo-•""°'".,..,. "I""""""'"' h ""' ,ho i..~ .... , """'"
`to h< °"'"""' hy P>tr-lO«Ju.< ..,i,... If "" o,du,!.. all ou1,Me ,001><1,,
`Or.ot "'" b, J,..,r,1, ll l,rothcr oh,, lnt<clllil)," for whloh •h• toond i, lil«ly
`..,.., om pu,h die intensHY d""" to 11,,q,olnt wh""' rho .,.,.,,d con )u!lt
`bc>rely be be,,d. Thi5 OI "'lled the 10ll.'/h,M i.itMl!eg. lb ,-.J.,, w.N!,
`,.;th the lndMdua.l ilslener, &rul aven.geo about ~X JO-" .,.tt, per
`"lua,,, mr:te, al HJOO herti. flow"'"'• the dueoh<,ld cau •o,y by a,
`rnueh a,• r.cro.r of"'" ,;tho, "--.y. J""'1'LJ.lllg on W<l !ndil'ldu>L Slnoe
`!t "'"""' <11cb a wlde "'"~"' th<: 1»11.-.nlo.,>I hgur< .r IQ·-" w.ut, P<•
`"'l""'c "'""'' b"' boon ,h...., u tbo notlll•r<I ol rdercn0<,"
`In tho <>11,., dl!'oction. "'"'""' ""'l' luud ,oundf, ii "' • mall<t of
`"hot lho oo., con ,ndure. !f we ,..r1 I"'"' th> Agan, JO-• w•tt• pOr
`
`""""" mell'r •nd '""""""' Ibo !toten.Sily. w~ ~,,d lh;t .1, • ..., •houl"""
`wo(t per"'!"""' meter ••nmd pn,,Ju,,... octi11I plo)'llulogi""l f~linJ or
`!kkling h, tho oar, IUld •< higher lm~f~ of ''"'era) ... 11, per ,qtate
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`MZ Audio, Ex. 2001, Page 18 of 31
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`

`

`9;
`
`Tl11 H<'t,q1tio11 nf ,\fo~im! Smmd~
`
`trn'h>r lhc ,ound prodn,:,,,~ phys-iolo1;1c.ol pain. A liguu cf (lne wntt
`per sgu.u-e mder ma) tJ1i,11 be ul.en a., a ueu·~a,y upl)tr limit le
`sou.:id intensity.
`lnr.·u,ily I, ,.,.r, Drdbci.
`111 Jl,,. ,lisrn~•.1011 ull()V~ "' rd.il•'rl I}, mmicd .des<riplion of a
`111ncl
`s~nsalll1n In 1!.s 111h•n\1!)' c.r 11,t• !<1und i11 ... -~11, l" r J'l""'" mcttt. Th~
`t. oot "<"f'Y pradii,.,J, "-~p!'ciallr for mu~lclam• tho rt h'll'!rnt •10-• wntts
`pc-r 11111"' mrt<'r• wm,ld not mr.;i,n much lD rno,;t p<-Oplt•. \Vf' ronld we
`th~ thrr-1hnl!l int,,nsity 31 Q dutinM pciinl. and correlfltci the &nnDd .se~,(cid:173)
`sittioo with the fa.:ttlr by whic,b the gi\'l'D ~ooud is more Intense than
`the thresh.old; that is. if I ,, the JOQund inll'n111y ,uJLl I Is th,: thre.ihold
`mt,m>1t. "t' would LL'le the rll-ho J,1 0 a, 11 n,,,;isw.,, Por t •• PPP
`wunu <•I 10 • ,,all> pc"I' squ,ire meti,r ,1,._
`,~I.lo l\'Uu}J b..• JO', that i'I,
`llu., smmu wauW Ix b:n thun,,uud 11111<' 1h
`tllle,.l1<1ld it1tr11S1ty. Simi(cid:173)
`I rlr, ih,• ff/ ,i;ound w1>uld bi, 1(114 ur l,10 bill1y11 time• the 11,:r)hold In•
`I, "''t)' Thi 1, ul>\'lomly
`ratl1c'1' ,·uinl~·r1<1rn~ rrJIJl'Jr11I 11011 also.
`111 tin nl,11"' uumli<'n, tlw import.int •iu 11tity is 1111 pow['! 1,f 1,•n
`1•1 t•11r~. Tit is l!\lggests tlL'lt "' '"" l1Jgaritl,111,. ( TlH ,. m work rd
`lls1i
`'"" i11 1hr At>Jlt nnf ) .\ ,·r11· u,C"fol mrasurc of a 1111..J ,s thrn a(cid:173)
`pn•~ ,·11111 h-rm~ of its mlr.PJS1lr1 /1,i~/ If wr rl=•e thit by I.., 1t t. d~(cid:173)
`firn,d a, lollo\\s:
`
`(1)
`
`Th 11nit of intcn<ilv l•'l·pl 1~ th,· tkrlbel, nh1irevia~ dB.
`From this definition wr obtain qulto a 11,ef ul «:ale with which ro
`mearure scru1iru. 11 we apply F.q. (1) to th<.· eiample,; worked out in
`tl:1t, pr€'\io11s 1ec;uon, we !';et the remits hown III I 'able I. rhls ~ves
`the le,d l>l tl11: tlut'Ml<lfd ai he.uiug as ~ru dooblc, "b!t:b K-cms
`
`I
`TAm
`!>oimd intt'n<.1t11~, '<J)r .. s~-~ 111 Ci'('loel,;
`1\-'TTO [ /J•
`(NIT.'ll!ifTI', V\~ /m'
`
`"lbm1wld
`o[ fl'll!lini:;
`fff
`t
`p
`f>IIP
`Thr~ hold
`of he~ring
`
`JO'
`lit •
`10 4
`10-•
`10-~
`
`10-u
`
`10'1
`10'•
`10•
`,no
`10•
`
`~a
`100
`80
`60
`-10
`
`0
`
`MZ Audio, Ex. 2001, Page 19 of 31
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